Linear and Integer Programming

Gilbert Strang.
Linear Algebra and its Applications. Third Edition.
Chapter 8 (Linear programming and game theory).
This is the most concise and clear introduction to the simplex method I
have read
and it also contains a short description of Karmakar's interior-point method.
If you have another source you have already used and feel comfortable with,
feel free to read it instead.

Linear
Programming 2 (Steven Czerwinski). Scribe notes on interior-point
methods from a previous version of the course.

E. L. Johnson and G. L. Nemhauser.
Recent developments and future directions in mathematical programming.
This is a good overview of optimization techniques including both linear
and integer programming.